Related papers: An efficient global optimization algorithm for max…
We study quantum algorithms for approximating Lasserre's hierarchy values for polynomial optimization. Let $f,g_1,\ldots,g_m$ be real polynomials in $n$ variables and $f^\star$ the infimum of $f$ over the semialgebraic set $S(g)=\{x:…
In many global Optimization Problems, it is required to evaluate a global point (min or max) in large space that calculation effort is very high. In this paper is presented new approach for optimization problem with subdivision labeling…
Bayesian optimization has recently emerged as a popular method for the sample-efficient optimization of expensive black-box functions. However, the application to high-dimensional problems with several thousand observations remains…
This paper investigates accelerating the convergence of distributed optimization algorithms on non-convex problems. We propose a distributed primal-dual stochastic gradient descent~(SGD) equipped with "powerball" method to accelerate. We…
We present a globally convergent SQP-type method with the least constraint violation for nonlinear semidefinite programming. The proposed algorithm employs a two-phase strategy coupled with a line search technique. In the first phase, a…
In this paper, we propose a framework based on the Retrospective Approximation (RA) paradigm to solve optimization problems with a stochastic objective function and general nonlinear deterministic constraints. This framework sequentially…
Random projection has been widely used in data classification. It maps high-dimensional data into a low-dimensional subspace in order to reduce the computational cost in solving the related optimization problem. While previous studies are…
This paper presents a first-order distributed algorithm for solving a convex semi-infinite program (SIP) over a time-varying network. In this setting, the objective function associated with the optimization problem is a summation of a set…
In a recent work, we presented the reduced Jacobian method (RJM) as an extension of Wolfe's reduced gradient method to multicriteria (multiobjective) optimization problems dealing with linear constraints. This approach reveals that using a…
A thesis submitted for the degree of Doctor of Philosophy of The Australian National University. In this work we introduce several new optimisation methods for problems in machine learning. Our algorithms broadly fall into two categories:…
This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…
This paper presents a methodology for using varying sample sizes in sequential quadratic programming (SQP) methods for solving equality constrained stochastic optimization problems. The first part of the paper deals with the delicate issue…
A large number of problems in optimization, machine learning, signal processing can be effectively addressed by suitable semidefinite programming (SDP) relaxations. Unfortunately, generic SDP solvers hardly scale beyond instances with a few…
We introduce BayeSQP, a novel algorithm for general black-box optimization that merges the structure of sequential quadratic programming with concepts from Bayesian optimization. BayeSQP employs second-order Gaussian process surrogates for…
We address the problem of how to achieve optimal inference in distributed quantile regression without stringent scaling conditions. This is challenging due to the non-smooth nature of the quantile regression (QR) loss function, which…
We suppose the existence of an oracle which solves any semidefinite programming (SDP) problem satisfying Slater's condition simultaneously at its primal and dual sides. We note that such an oracle might not be able to directly solve general…
This paper proposes a quantum computing-based algorithm to solve the single image super-resolution (SISR) problem. One of the well-known classical approaches for SISR relies on the well-established patch-wise sparse modeling of the problem.…
Super-resolution (SR) is a promising tool for generating high-fidelity simulations of physical systems from low-resolution data, enabling fast and accurate predictions in engineering applications. However, existing deep-learning based SR…
We develop new algorithms for Riemannian bilevel optimization. We focus in particular on batch and stochastic gradient-based methods, with the explicit goal of avoiding second-order information such as Riemannian hyper-gradients. We propose…
We study generalization properties of distributed algorithms in the setting of nonparametric regression over a reproducing kernel Hilbert space (RKHS). We first investigate distributed stochastic gradient methods (SGM), with mini-batches…